When I think drape I think silk, SeaCell, or bamboo. I don't think cotton, especially the smooth, sorta stiff mercerized cotton yarn that's ubiquitous in spring and summer knits.
But I'm thinking again because Kristin Ohmdahl and Eunny Jang, hosts of Knitting Daily TV, are here to show us all how to knit with cotton and get the drape we want. With the right shaping and pattern, you can get a great result.
Here is a great video clip from Knitting Daily showing many ways to incorporate drape while using your cotton yarns!